CSC 405 Introduction to Computer Security

1. CSC 405Introduction to Computer Security Topic 2. Basic Cryptography (Part I) By Dr. Peng Ning

2. Cryptography • Cryptography • Original meaning: The art of secret writing • Becoming a science that relies on mathematics (number theory, algebra) • Process data into unintelligible form, reversible, without data loss • Usually one-to-one (not compression) By Dr. Peng Ning

3. Encryption/Decryption • Plaintext: a message in its original form • Ciphertext: a message in the transformed, unrecognized form • Encryption: the process that transforms a plaintext into a ciphertext; also known as encode and encipher • Decryption: the process that transforms a ciphertext to the corresponding plaintext; also known as decode and decipher • Key: the value used to control encryption/decryption • Cryptosystem: a system for encryption and decryption plaintext ciphertext plaintext encryption decryption key key By Dr. Peng Ning

4. Cryptanalysis • Ciphertext only: • Analyze only with the ciphertext • Example: Exhaustive search until “recognizable plaintext” • Smarter ways available • Known plaintext: • Secret may be revealed (by spy, time), thus <ciphertext, plaintext> pair is obtained • Great for mono-alphabetic ciphers By Dr. Peng Ning

5. Cryptanalysis (Cont’d) • Chosen plaintext: • Choose text, get encrypted • Useful if limited set of messages • Chosen ciphertext: • Choose ciphertext • Get feedback from decryption, etc. By Dr. Peng Ning

6. Simple Forms of Encryption • Substitutions • One letter is replaced with another • Transpositions • Also called permutations • The order of the letters is rearranged • Building blocks of modern cryptographic algorithms By Dr. Peng Ning

7. Substitution Ciphers • Monoalphabetic cipher (simple substitution) • Use a correspondence table • Substitute a character or symbol for each character of the original message • Example: Caesar cipher • Replace each letter with the one 3 letters later • Exercise • E (“COMPUTER SCIENCE”)  • D (“qf vwdwh”)  By Dr. Peng Ning

8. Caesar Cipher • Cryptanalysis of Caesar cipher • Can be done by guessing • Clues • Break between two words is preserved • You can try common letters starting or ending a word • Double letters are preserved • Always use the same mapping • Exercise: • wklv phvvdjh lv qrw wrr kdug wr euhdn By Dr. Peng Ning

9. Other Substitutions • In general • The alphabet is scrambled • Each plaintext letter maps to a unique ciphertext letter • A substitution table can be defined using a permutation • A permutation is a reordering of the elements of a sequence By Dr. Peng Ning

10. Cryptanalysis of Substitution Ciphers • Ad hoc clues • Short words, words with repeated patterns, common initial and final letters • Language specific knowledge • Frequency of letters • E, T, O, and A occur far more often than J, Q, X, and Z • Letter patterns • th, er, en, ss, st, … By Dr. Peng Ning

11. One-Time Pads • Encrypt plaintext with a large, non-repeating set of keys • Absolute synchronization between sender and receiver • Unlimited number of keys Vernam cipher By Dr. Peng Ning

12. Book Cipher • Use book, piece of music, or other object with which structure can be analyzed • Both sender and receiver need access to identical objects • Example: book cipher with Vigenère tableau • Key: I am, I exist, that is certain. • Plaintext: MACHINES CANNOT THINK column iamie xistt hatis cert MACHI NESCA NNOTT HINK row Uaopm kmkvt unbhl jmed By Dr. Peng Ning

13. a b c d e f g h i j k l m n o p q r s t u v w x y z A a b c d e f g h i j k l m no p q r s t u v w x y z B b c d e f g h i j k l m n o p q r s t u v w x y z a C c d e f g h i j k l m n o p q r s t u v w x y z a b D d e f g h i j k l m n o p q r s t u v w x y z a b c E e f g h i j k l m n o p q rs t u v w x y z a b c d F f g h i j k l m n o p q r s t u v w x y z a b c d e G g h i j k l m n o p q r s t u v w x y z a b c d e f H h i j k l m n o p q r s t u v w x y z a b c d e f g I i j k l m n o p q r s t u vw x y z a b c d e f g h J j k l m n o p q r s t u v w x y z a b c d e f g h i K k l m n o p q r s t u v w x y z a b c d e f g h i j L l m n o p q r s t u v w x y z a b c d e f g h i j k M m n o p q r s t u v w x y z a b c d e f g h i j k l … Vigenère Tableau By Dr. Peng Ning

14. Cryptanalysis of Book Cipher • Flaw of book cipher • Distributions of both key and message cluster around high frequency letters • Example • A, E, O, T, N, I account for 50% of all letters • Probability of both key and plaintext letters are one of them: 0.25 • Cryptanalysis • Look for intersections of the above six letters • For each cipher text letter, identify the possible plaint text letter from those intersections uaopm kmkvt unbhl jmed ?AA?E ?E??A ?ANN? ?EA? O I I T NTTIE T T T Correct prediction underlined By Dr. Peng Ning

15. Transpositions (Permutations) • Letters of the message are rearranged • Aim to break established patterns • Confusion and diffusion • Confusion • Make it difficult to determine how message and key are transformed into cipher text • Complex relationship between plaintext, key, and ciphertext • Done through substitution • Diffusion • Widely spread the information from the message or key across the cipher text • Done through transposition (permutation) By Dr. Peng Ning

16. Columnar Transpositions • Rearrange characters of the plain text into columns Cipher text: ______________________________________ By Dr. Peng Ning

17. Cryptanalysis of Transpositions • Diagram analysis • Frequent diagram • Patterns of pairs of adjacent letters • RE, EN, ER, NT, … • Frequent trigrams • Groups of three letters • ENT, ION, AND, ING, … • Infrequent diagrams and trigrams • VK and QP By Dr. Peng Ning

18. Cryptanalysis by Diagram Analysis • Confirms it is a transposition • Compute the letter frequencies • Find adjacent columns • Try different column sizes • Look for common diagrams • Verify possible matches for different positions • Rely heavily on a human’s judgment of what “looks right” By Dr. Peng Ning

19. Product Cipher • Product cipher • Combination of two ciphers • Modern ciphers: interleaved substitutions and transpositions (permutations) • SPSP… • But • How about SPSSP… • How about SPPS… By Dr. Peng Ning

20. “Good” Encryption algorithms • What does it mean for a cipher to be “good”? • Meaning of “good” depends on intended use of the cipher • Commercial applications • Military applications By Dr. Peng Ning

21. Characteristics of “Good” Ciphers • Shannon’s principles • The amount of secrecy needed should determine the amount of labor appropriate for the encryption and decryption • The set of keys and the enciphering algorithm should be free from complexity • No restrictions on keys or plain text; keys should be short • The implementation of the process should be as simple as possible • Formulated with hand encryption in mind • Implementation on a computer need not be simple, as long as the time complexity is tolerable By Dr. Peng Ning

22. Characteristics of “Good” Ciphers • Shannon’s Principles (Cont’d) • Errors in ciphering should not propagate and cause corruption of further information in the message • No error propagation • The size of the enciphered text should be no larger than the text of the original message • Dramatic cipher expansion in size does not carry more information, but • It gives the cryptanalyst more data to infer patterns By Dr. Peng Ning

23. Security of An Encryption Algorithm • Unconditionally secure • It is impossible to decrypt the ciphertext • One-time pad (the key is as long as the plaintext) • Computationally secure • The cost of breaking the cipher exceeds the value of the encrypted information • The time required to break the cipher exceeds the useful lifetime of the information By Dr. Peng Ning

24. Secret Keys v.s. Secret Algorithms • Security by obscurity • We can achieve better security if we keep the algorithms secret • Hard to keep secret if used widely • Reverse engineering, social engineering • Publish the algorithms • Security of the algorithms depends on the secrecy of the keys • Less unknown vulnerability if all the smart (good) people in the world are examine the algorithms By Dr. Peng Ning

25. Secret Keys v.s. Secret Algorithms (Cont’d) • Commercial world • Published • Wide review, trust • Military • Keep algorithms secret • Avoid giving enemy good ideas • Military has access to the public domain knowledge anyway. By Dr. Peng Ning

26. Types of Cryptography • Number of keys • Hash functions: no key • Secret key cryptography: one key • Public key cryptography: two keys - public, private • The way in which the plaintext is processed • Block cipher: divides input elements into blocks • Stream cipher: process one element (e.g., bit) a time By Dr. Peng Ning

27. Secret Key Cryptography • Same key is used for encryption and decryption • Also known as • Symmetric cryptography • Conventional cryptography plaintext ciphertext plaintext encryption decryption key Same key key By Dr. Peng Ning

28. Secret Key Cryptography (Cont’d) • Basic technique • Product cipher • Multiple applications of interleaved substitutions and permutations • Cipher text approximately the same length as plaintext S P S P S plaintext ciphertext … key By Dr. Peng Ning

29. Stream and Block Ciphers • Stream ciphers • Convert one symbol of plaintext immediately into a symbol of ciphertext • A symbol: a character, a bit • Examples • Substitution ciphers discussed earlier • Modern example: RC4 By Dr. Peng Ning

30. Stream and Block Ciphers (Cont’d) • Block cipher • Encrypt a group of plaintext symbols as on block • Examples • Columnar transposition • Modern examples: DES, AES By Dr. Peng Ning

31. Applications of Secret Key Cryptography • Transmitting over an insecure channel • Challenge: How to share the key? • Secure Storage on insecure media • Authentication • Challenge-response • To prove the other party knows the secret key • Must be secure against chosen plaintext attack • Integrity check • Message Integrity Code (MIC) • Also called Message Authentication Code (MAC) By Dr. Peng Ning

32. Public Key Cryptography • Invented/published in 1975 • A public/private key pair is used • Public key can be publicly known • Private key is kept secret by the owner of the key • Much slower than secret key cryptography • Also known as • Asymmetric cryptography plaintext ciphertext plaintext encryption decryption Public key Private key By Dr. Peng Ning

33. Public Key Cryptography (Cont’d) • Another mode: digital signature • Only the party with the private key can create a digital signature. • The digital signature is verifiable by anyone who knows the public key. • The signer cannot deny that he/she has done so. message Yes/No Digital signature Sign Verify Private key Public key By Dr. Peng Ning

34. Applications of Public Key Cryptography • Data transmission • Alice encrypts ma using Bob’s public key eB, Bob decrypts ma using his private key dB. • Storage • Can create a safety copy: using public key of trusted person. • Authentication • No need to store secrets, only need public keys. • Secret key cryptography: need to share secret key for every person to communicate with. By Dr. Peng Ning

35. Applications of Public Key Cryptography (Cont’d) • Digital signatures • Sign hash H(m) with the private key • Authorship • Integrity • Non-repudiation: can’t do with secret key cryptography • Key exchange • Establish a common session key between two parties By Dr. Peng Ning

36. Hash Algorithms • Also known as • Message digests • One-way transformations • One-way functions • Hash functions • Length of H(m) much shorter then length of m • Usually fixed lengths: 128 or 160 bits Message of arbitrary length A fixed-length short message Hash H By Dr. Peng Ning

37. Hash Algorithms (Cont’d) • Desirable properties of hash functions • Performance: Easy to compute H(m) • One-way property: Given H(m) but not m, it’s difficult to find m • Weak collision free: Given H(m), it’s difficult to find m’ such that H(m’) = H(m). • Strong collision free: Computationally infeasible to find m1, m2 such that H(m1) = H(m2) By Dr. Peng Ning

38. Applications of Hash Functions • Primary application • Generate/verify digital signature H(m) Message m Signature Sig(H(m)) H Sign Private key Message m H(m) H Verify Yes/No Signature Sig(H(m)) Public key By Dr. Peng Ning

39. Applications of Hash Functions (Cont’d) • Password hashing • Doesn’t need to know password to verify it • Store H(password+salt) and salt, and compare it with the user-entered password • Salt makes dictionary attack more difficult • Message integrity • Agree on a secrete key k • Compute H(m|k) and send with m • Doesn’t require encryption algorithm, so the technology is exportable By Dr. Peng Ning

40. DES (Data Encryption Standard) • Officially adopted in 1976 • Expired in 1998 • Key: 64 bit quantity=8-bit parity+56-bit key • Every 8th bit is a parity bit. • 64 bit input, 64 bit output. 64 bit M 64 bit C DES Encryption 56 bits By Dr. Peng Ning

41. DES Top View 56-bit Key 64-bit Input Generate keys Initial Permutation Permutation 48-bit K1 Round 1 48-bit K2 Round 2 …... 48-bit K16 Round 16 Swap Swap 32-bit halves Final Permutation Permutation 64-bit Output By Dr. Peng Ning

42. Bit Permutation (1-to-1) 1 2 3 4 32 ……. 0 0 1 0 1 Input: 1 bit Output …….. 1 0 1 1 1 22 6 13 32 3 By Dr. Peng Ning

43. Initial and Final Permutations • Initial permutation (IP) • View the input as M: 8 X 8 bit matrix • Transform M into M’ in two steps • Transpose row x into column (9-x), 0<x<9 • Apply permutation on the rows: • For even row y, it becomes row y/2 • For odd row y, it becomes row (5+y/2) • Final permutation FP = IP-1 By Dr. Peng Ning

44. Per-Round Key Generation Initial Permutation of DES key C i-1 D i-1 28 bits 28 bits Circular Left Shift Circular Left Shift Round 1,2,9,16: single shift Others: two bits Permutation with Discard 48 bits Ki C i D i 28 bits 28 bits By Dr. Peng Ning

45. A DES Round 32 bits 32 bits E-Boxes Ki One Round Encryption 48 bits Mangler Function S-Boxes P 32 bits 32 bits 32 bits By Dr. Peng Ning

46. E Box of DES (Expansion Permutation) • How is the E box defined • Each row expands from 4 bits to 6 bits By Dr. Peng Ning

47. 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 S1 S2 S3 S4 S5 S6 S7 S8 + + + + + + + + Another View of the Mangler Function subkey The permutation produces “spread” among the chunks/S-boxes! Permutation By Dr. Peng Ning

48. 2 bits row I1 I2 I3 I4 I5 I6 S O1 O2 O3 O4 i an integer between 0 and 15. 4 bits column = 1,…8. i S-Box (Substitute and Shrink) • 48 bits ==> 32 bits. (8*6 ==> 8 *4) • 2 bits used to select amongst 4 permutations for the rest of the 4-bit quantity By Dr. Peng Ning

49. The First S Box S1 Each row and column contain different numbers. 0 1 2 3 4 5 6 … 15 0 14 4 13 1 2 15 11 1 0 15 7 4 14 2 13 2 4 1 14 8 13 6 2 3 15 12 8 2 4 9 1 Example: input: 100110 output: ??? By Dr. Peng Ning

50. Cipher Iterative Action Input: 64 bits Key: 48 bits Output: 64 bits Key Generation Box Input: 56 bits Output: 48 bits DES Standard One round (Total 16 rounds) By Dr. Peng Ning